Heat a large nonstick skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. While the skillet heats up, chop up the cooked potatoes into bite-size chunks then add to the hot skillet and spread out in an even layer. Season them with a little salt and pepper, and let them brown for about 2 minutes without messing with them. Then give them a stir and continue to brown them for another 3-4 minutes, stirring every now and then.
Add the chopped pepper and onions, stir to combine and continue to cook for 4-5 minutes or until the veggies are tender. Add the leftover chili and cook until it is heated through.
While the leftover chili is heating up with the potatoes, start the eggs: Preheat another skillet over medium-high heat with 2 tablespoons of butter. Once the butter has melted and the bubbles have subsided, crack eggs into the pan, season with salt and pepper, and fry to desired doneness.
Divide the chili hash between 4 serving plates and top with the fried egg.